Chromatic equivalence classes of certain generalized polygon trees, III

Chromatic equivalence classes of certain cycles with edges

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G∼H , if P(G) = P(H). A graph G is chromatically unique if for any graph H , G∼H implies that G is isomorphic with H . In this paper, we give the necessary and su:cient conditions for a family of generalized polygon trees to be chromatically unique. c © 2001 Elsevier Science B.V. All ...

Some equivalence classes of operators on B(H)

FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

Characterizations of generalized polygons and opposition in rank 2 twin buildings

In this paper, we characterize the natural opposition relation on the set of flags of a generalized polygon. We also investigate when a certain relation on any rank 2 geometry of finite diameter is equivalent to the opposition relation in a generalized polygon. As a consequence we obtain a new definition of generalized polygons. Finally, we also characterize the opposition relation in twin tree...

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...